(a) A person drinks four glasses of cold water (3.0°C) every day. The volume of each glass is 2.5x10^2 mL. How much heat (in kJ) does the body have to supply to raise the temperature of the water to 37°C, the body temperature? (b) How much heat would your body lose if you were to ingest 8.0x10^2 g of snow at 0°C tp quench thirst?
a)
q = mass H2O x specific heat H2O x (Tfinal-Tinitial)
q will be in J, convet to kJ.
b)
q = (mass snow x heat fusion) + [mass melted snow x specific heat H2O x (Tfinal-Tinitial)]
Tfinal = 37
Tinitial = 0
345
To find the amount of heat the body has to supply in each case, we will use the specific heat capacity formula:
q = mcΔT
where q is the heat transfer (in joules), m is the mass (in grams), c is the specific heat capacity (in J/g°C), and ΔT is the change in temperature (in °C).
(a) To find the amount of heat required to raise the temperature of 4 glasses of cold water (3.0°C) to body temperature (37°C):
Step 1: Convert the volume of each glass to the mass of water using density.
Density of water = 1 g/mL
Volume of each glass = 2.5x10^2 mL
Mass of water in each glass = Volume x Density
= 2.5x10^2 mL x 1 g/mL
= 2.5x10^2 g
Step 2: Calculate the total mass of water for 4 glasses.
Total mass of water = Mass of water in each glass x Number of glasses
= 2.5x10^2 g x 4
= 1x10^3 g
Step 3: Calculate the change in temperature.
ΔT = Final temperature - Initial temperature
= 37°C - 3.0°C
= 34°C
Step 4: Use the specific heat capacity of water.
Specific heat capacity of water = 4.18 J/g°C (approximately)
Step 5: Substitute the values into the formula.
q = mcΔT
= 1x10^3 g x 4.18 J/g°C x 34°C
= 1.43x10^5 J
To convert the result to kilojoules (kJ), divide by 1000:
q = 1.43x10^5 J / 1000
= 143 kJ
Therefore, the body has to supply approximately 143 kJ of heat to raise the temperature of the water to 37°C.
(b) To find the amount of heat lost when ingesting 8.0x10^2 g of snow at 0°C:
Step 1: Calculate the change in temperature.
ΔT = Final temperature - Initial temperature
= 0°C - 37°C
= -37°C
Step 2: Use the specific heat capacity of water (since snow is essentially frozen water).
Specific heat capacity of water = 4.18 J/g°C
Step 3: Substitute the values into the formula.
q = mcΔT
= 8.0x10^2 g x 4.18 J/g°C x (-37°C)
= -1.17x10^5 J
To convert the result to kilojoules (kJ), divide by 1000:
q = -1.17x10^5 J / 1000
= -117 kJ
Therefore, the body would lose approximately 117 kJ of heat if you were to ingest 8.0x10^2 g of snow at 0°C. Note that the negative sign indicates heat loss.